SOLUTION: Compute the value of the discriminant and give the number of real solutions of the quadratic equation. 3x^2-7x+4=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Compute the value of the discriminant and give the number of real solutions of the quadratic equation. 3x^2-7x+4=0      Log On


   

Question 639979: Compute the value of the discriminant and give the number of real solutions of the quadratic equation.
3x^2-7x+4=0
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Compute the value of the discriminant and give the number of real solutions to the quadratic equation:
3x^2 - 7x + 4 = 0

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-7x%2B4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-7%29%5E2-4%2A3%2A4=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+1+%29%29%2F2%5C3+=+1.33333333333333
x%5B2%5D+=+%28-%28-7%29-sqrt%28+1+%29%29%2F2%5C3+=+1

Quadratic expression 3x%5E2%2B-7x%2B4 can be factored:
3x%5E2%2B-7x%2B4+=+3%28x-1.33333333333333%29%2A%28x-1%29
Again, the answer is: 1.33333333333333, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-7%2Ax%2B4+%29